<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; = charset=iso-8859-1"> <META content="MSHTML 6.00.2900.2627" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV><FONT face=Arial size=2>Joe,</FONT></DIV> <DIV><FONT face=Arial size=2>The "standard" 12-TET takes 1/12 of the = pythagorean comma from the fifths.</FONT></DIV> <DIV> <DIV><FONT face=Arial size=2>The pure fifth approach you talked = about, puts the pythagorean comma in 1/7 up to the octave to get pure = fifths.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>In the pure 12ths approach, i published = in 1988, the 12 fifths are split up to 12 twelfths and 12 octaves, yielding a = circle of 12 twelfths on one side and 19 octaves at the other side.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>The pure 12ths approach we are talking = about here, and for which already exists various (free) approaches, puts then a = 1/19 of the pythagorean comma to the 19 octaves. C</FONT><FONT face=Arial = size=2>omplete different thing to the Cordier /Coleman thing.</FONT></DIV> <DIV><FONT face=Arial size=2>And the existing approaches have some = serious problems to be realized, even with ETD.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>In my new approach every fifth = (smaller than pure, not pure)and every octave (stretched , not pure) having 1 = note together (formig a 3-note chord, there are four such combinations) = can sound pure, when played together and tuned correctly.This = is due to my recent discovery, that there is a symmetry of the = beat ratios to the interval ratios only in the P12th = tuning.</FONT></DIV> <DIV> </DIV> <DIV><FONT face=Arial size=2>so the complete temperament will = set or calculated by tuning/calculating the next note by reffering to two = previous notes forming such a 3-note combination.</FONT></DIV> <DIV><FONT face=Arial size=2>And this <U>method</U> is new, and that = is what i filed for patenting. One can not patent maths or an idea or a system, = but a method you can.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>regards,</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Bernhard</FONT></DIV></DIV> <BLOCKQUOTE dir=ltr style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black"><B>From:</B> <A title=joegarrett@earthlink.net = href="mailto:joegarrett@earthlink.net">Joe Garrett</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A = title=pianotech@ptg.org href="mailto:pianotech@ptg.org">pianotech</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Friday, April 15, 2005 = 6:59 AM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: Jim Coleman's = temperaments was Pure.....</DIV> <DIV><BR></DIV> <DIV><FONT face=Arial size=2>Bill Ballard asked: "<FONT = face="Times New Roman" size=3>Joe, just for historical purposes, which of the many tuning = schemes <BR>Jim has handed out over the years, are you referring to? And of <BR>course, Bernhard has only given us a rough sketch of the aural = <BR>version of his temperament"</FONT></FONT></DIV> <DIV> </DIV> <DIV><FONT face=Arial size=2>Bill,</FONT></DIV> <DIV><FONT face=Arial size=2>There have been several, but the one = I was referring to was an article in the PTJ a few years back. All based on = the perfect 5th, etc. IMO, pretty much the same thing. Just presented in a = different way. Patenting a temperament? Harumph I say! Utter B.S.! Tis = better to just publish and show the world a different way, that may have some = validity, (only to be proven with time tested = procedures).</FONT></DIV> <DIV><FONT face=Arial size=2>Regards,</FONT></DIV> <DIV><FONT face=Arial size=2>Joe Garrett, R.P.T.<BR>Captain, Tool Police<BR>Squares R I</FONT></DIV></BLOCKQUOTE></BODY></HTML>